Exploring Realized Higher Moment Measures on the S&P/BMV IPC Index
To estimate daily volatility of equity returns, we can use the intraday data, in particular, the intraday returns. Since the expected value of the intraday returns is zero, a good estimator of variance is the sum of the squared returns.
We can now compute the realized variance for each day:
# A tibble: 5,607 x 3
index_date RV RVol
<date> <dbl> <dbl>
1 1996-01-02 0.000180 0.213
2 1996-01-03 0.000272 0.262
3 1996-01-04 0.0000380 0.0979
4 1996-01-05 0.0000422 0.103
5 1996-01-08 0.0000218 0.0740
6 1996-01-09 0.0000478 0.110
7 1996-01-10 0.0000542 0.117
8 1996-01-11 0.0000553 0.118
9 1996-01-12 0.0000538 0.116
10 1996-01-15 0.0000367 0.0962
# ... with 5,597 more rows
Now let’s plot the RVs:
Let’s check the ACF on the RVs:
An RV Sparse estimator consists of calculating the realized variance but with a sample that is less frequent than the 1-minute grid. Instead, it is sampled in an s-minute grid (where \(s \geq 1\)).
Here, we will use different combinations of \(s\) such as s = 5,
s = 10, s = 15, and s = 30. In
order to plot a signature plot, we will also sample from \(s \in [1, 120]\).